Multiparametric bifurcation analysis of a basic two stage population model
Baer, S. M., Kooi, B. W., Kuznetzov, Yu. A. and Thieme, H. R. 2006.
Multiparametric bifurcation analysis of a basic two stage population model.
SIAM Applied Mathematics : subm. 2005/03/01
Abstract
In this paper we investigate long-term dynamics of the most basic
model for stagestructured populations, in which the per capita
transition from the juvenile into the adult class is density
dependent. The model is represented by an autonomous system of two
nonlinear differential equations for a single population. We nd that
the interaction of intra-adult competition and intrajuvenile
competition gives rise to multiple attractors, one of which can be
oscillatory. A detailed numerical study reveals a rich bifurcation
structure for this two dimensional system, whose organizing center
is a degenerate Bogdanov-Takens (BT) bifurcation point. The
corresponding triple critical equilibrium has an elliptic sector,
which is demonstrated by the numerical normal form analysis. It is
shown that the canonical unfolding of the codim-three BT point
reveals the underlying dynamics of the model. Certain new features
of this unfolding, which are important in applications but have been
overlooked in available theoretical studies, are
established. Various three-, two-, and one-parameter bifurcation
diagrams of the model are presented and interpreted in biological
terms.